The ability to recall the answers to math equations is touted as a spark of genius and a primary goal for many elementary school children. Memorizing numbers, carrying remainders, and long handing "all-the-things" is the norm but this is not the optimal nor the most efficient way to learn math.
Instead of learning the answers or long and convoluted procedures we need to teach both children and adults how to calculate. That there is not only one way to arrive at the correct answer.
It's this relationship with numbers that many miss, that I missed growing up. It's all because I stumbled across Scott Flansburg, that I am not trying to avoid basic arithmetic for the first time in my life.
I used to say "why should I do math when I can make the computer do it?"
Start at Zero
Scott explains that there is no ten digit. Ten is a number but only by combining the zero digit and the one digit. By starting with zero instead of one we can understand numbers from a natural perspective.
That tickles my programmer's heart
The method Scott uses for addition simplifies the entire process and eliminates longhand as most of us were taught. Instead of carrying numbers and writing down a ton of steps. All we need to do is reverse our direction. Instead of adding from right to left he tells us to add from left to right. Just like reading:
Let's take 32 and add 43. Now adding from left to right we start with adding 30 and 40; that's 70. Now add 2, that's 72 then 3 for the final number of 75.
Much more relaxed than carrying and much faster, especially for estimations.
Subtraction is the same as addition but backwards.
Let's take 63 and 47:
60 - 40 = 20 23 - 7 = 16 so that means: 63 - 47 = 16
Multiplication of numbers is (almost) as easy as the addition. I found these tricks from ofpad.com.
Single Digit Multipliers
All that we need to do is multiply from left to right.
63 * 4 6 * 4 = 24 3 * 4 = 12 240 + 12 = 252 63 * 4 = 252
When First Number Ends Higher Than 6
When a number to be multiplied ends is a 7, 8, or 9 the trick is to round up that number. Then multiply from left to right as above. After that multiply the amount rounded by the base number. Finally, subtract the second number from the first. It looks like this:
77 * 6 77 rounds to 80 80 * 6 = 480 3 * 6 = 18 (three is our rounded amount) 480 - 18 = 462
It's a bit more involved but still easier to understand than what most of us were taught growing up and what is taught today.
Two, Two-Digit Numbers
All we need to do in this trick is to take the second number in the problem and remove down to the nearest ten. Then multiply the first number by the new ten's based number and the amount we removed. Finally, we add them together:
34 * 65 Take the second number to the nearest ten: 34 * 60 30 * 60 = 1800 4 * 60 = 240 1800 + 240 = 2040 Now the bit we took off: 34 * 5 30 * 5 = 150 4 * 5 = 20 150 + 20 = 170 Now add them together! 2040 + 170 = 2210
For numbers ending in a 7 or higher do the rounding up method.
As Scott Flansburg said in a video I saw:
Division is just multiplication backwards.
This makes solving division in our heads easier for everyday tasks. Granted there are probably tricks to so solve massive division problems but for our every day, this mindset is much more helpful than writing it out.
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